Determine the value of $x$ in the given figure."

To do: To find the value of $x$ in the given fig.

Solution:

Lets Join $AB$.

As shown in the given fig. $AB||CD$

Therefore, $\angle BAC=\angle ACD=90^o$

In $\vartriangle AOC$,

$\angle OAC=\angle OAB-\angle BAC$

$=130^o-90^o=40^o$

$\angle OCA=\angle OCD-\angle DAC$

$=120^o-90^o$

$=30^o$

Therefore, $\angle AOC+\angle OAC+\angle OCA=180^o$     [Sum of the angles in triangle is $180^o$]

$\Rightarrow x+40^o+30^o=180^o$

$\Rightarrow x+70^o=180^o$

$\Rightarrow x=180^o-70^o$

$\Rightarrow x=110^o$

Thus, the value of $x$ is $110^o$.

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Updated on: 10-Oct-2022

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